Convergence radius of Halley’s method for multiple roots under center-Hölder continuous condition

Abstract

Recently, a new treatment based on Taylor’s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented. It has been successfully applied to enlarge the convergence radius of the modified Newton’s method and Osada’s method for multiple roots. This paper re-investigates the convergence radius of Halley’s method under the condition that the derivative f(m+1) of function f satisfies the center-Hölder continuous condition. We show that our result can be obtained under much weaker condition and has a wider range of application than that given by Bi et. al.(2011) [21].